16 March, 2016

GIS

Geographic Information Systems

GIS

Geographic Information Systems

  • incorporating
  • storing
  • manipulating
  • analyzing
  • displaying…

Spatial Data

What is spatial data?

Nonspatial data has no location information

nonspatial = data.frame(
  id=c(1,2,3,4),
  data=rnorm(4)
)
print(nonspatial)
##   id       data
## 1  1  1.1327954
## 2  2 -0.3140816
## 3  3 -0.2447371
## 4  4  0.7490857

What is spatial data?

Spatial data has location information

The simplest spatial data are points on a map

spatial = data.frame(
  id=c(1,2,3,4),
  data=rnorm(4),
  x=runif(4,-180,180),
  y=runif(4,-90,90)
)
print(spatial)
##   id       data          x          y
## 1  1 -0.3386280 -110.90702  16.393213
## 2  2  0.7831824  178.54540  -4.378136
## 3  3  0.4201943  153.38047 -39.811305
## 4  4  0.9755812  -94.22992 -43.465543

What is spatial data?

Which we can convert to explicitly spatial data using the sp package. Most GIS packages in R store data as sp classes.

library(sp)

What is spatial data?

The sp package has a method called coordinates that converts points to an sp class.

coordinates(spatial) = ~ x + y
class(spatial)
## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"
plot(spatial, axes=T)


What is spatial data?

Spatial data also needs a reference system or "projection" that allows us to represent spatial features on a map. Projections can be thought of as simply a coordinate system with an origin that is relative to a known point in space.

This is a whole field of mathematically intensive study termed "geodesy"

Much of the field of geodesy is jam-packed in the rgdal package, which is a wrapper for the Geospatial Data Abstration Library

library(rgdal)

What is spatial data?

rgdal includes a comprehensive list of projections that are typically represented as a string of parameters.

The most common is our standard latitude/longitude system, where the coordinates are angular and the origin is the equator directly south of Greenwich, England. The simplest projection string to denote this projections is:

"+proj=longlat"

To define the projection for spatial, we write to its proj4string slot:

proj4string(spatial) = "+proj=longlat"

Projections are a necessary evil for GIS users (to be continued)

What is spatial data?

With a projection associated with our spatial data, we can now relate it to other spatial data. In other words, let's make a map!

library(leaflet)
m = leaflet(data=spatial) %>%
  addTiles() %>%
  addMarkers()
m

What is spatial data?

Spatial data types

Spatial data types

Two main types: vector and raster

Vector = Polygons
Raster = Grid

Vector = Discrete
Raster = Continuous

Vector = Illustrator/Inkscape
Raster = Photoshop/GIMP







Vector Data

Vector Data Intro

  • How data is represented Vector data is represented by coordinate pairs,









Figure depicting * Points

  • Lines

  • Polygons

Vector Data Intro

Geometry is associated with other data, attribute data Conceptualize as a row in a table

  • What vector data is used for

Outline 2

Part I

  • introduce soils data, ways of looking at it

  • well data, read in and convert

  • plot the two, brief discuss issues with CRS matching

  • Example scenario, demo gIntersects and how to use introduce other types of spatial relations

  • Use over to extract attributes and select those above a threshold of sand

  • Introduce buffering and suggest trying with that

Vector Data Basics

Data Input/Output

library(rgdal)
soils = readOGR(
    dsn="data",
    layer="soilsData")
## OGR data source with driver: ESRI Shapefile 
## Source: "data", layer: "soilsData"
## with 75 features
## It has 27 fields
writeOGR(
    soils,
    "data",
    "soilsData_out",
    driver="ESRI Shapefile"
)

Vector Data Basics

Other ways of creating of spatial data from list of coordinates:

wells = read.delim("./data/WellLocations.tsv")
class(wells); head(wells)
## [1] "data.frame"
##           x        y pts.data.id
## 1 -90.05145 43.10047           1
## 2 -90.05553 43.10470           2
## 3 -90.07305 43.09013           3
## 4 -90.04716 43.08454           4
## 5 -90.07198 43.08850           5
## 6 -90.06599 43.09197           6
coordinates(wells) <- ~ x + y
class(wells)
## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"

Vector Data Basics

Helper functions:

class(soils)
## [1] "SpatialPolygonsDataFrame"
## attr(,"package")
## [1] "sp"
slotNames(soils)
## [1] "data"        "polygons"    "plotOrder"   "bbox"        "proj4string"
length(soils)
## [1] 75

Vector Data Basics

str(soils@data[,1:10])
## 'data.frame':    75 obs. of  10 variables:
##  $ mukey  : Factor w/ 25 levels "2774742","2774772",..: 12 19 12 6 9 5 7 24 25 13 ...
##  $ muarcrs: Factor w/ 75 levels "0.40538405","0.90105194",..: 30 62 70 18 8 26 19 5 15 23 ...
##  $ Sand1  : num  21.5 11 21.5 12 29.5 ...
##  $ Sand2  : num  35.29 8.34 35.29 9.02 38.22 ...
##  $ Sand3  : num  45.09 7.56 45.09 16.59 64.52 ...
##  $ Sand4  : num  48.6 30.6 48.6 36.7 33.2 ...
##  $ Sand5  : num  0 31.1 0 27.1 57.2 ...
##  $ Silt1  : num  45.8 65.2 45.8 68.7 54.5 ...
##  $ Silt2  : num  37.3 64.9 37.3 60.3 43.5 ...
##  $ Silt3  : num  36.7 64.1 36.7 34 21.1 ...

Vector Data Basics

str(soils@polygons[1])
## List of 1
##  $ :Formal class 'Polygons' [package "sp"] with 5 slots
##   .. ..@ Polygons :List of 1
##   .. .. ..$ :Formal class 'Polygon' [package "sp"] with 5 slots
##   .. .. .. .. ..@ labpt  : num [1:2] 514199 291168
##   .. .. .. .. ..@ area   : num 10776
##   .. .. .. .. ..@ hole   : logi FALSE
##   .. .. .. .. ..@ ringDir: int 1
##   .. .. .. .. ..@ coords : num [1:21, 1:2] 514211 514206 514195 514178 514180 ...
##   .. ..@ plotOrder: int 1
##   .. ..@ labpt    : num [1:2] 514199 291168
##   .. ..@ ID       : chr "0"
##   .. ..@ area     : num 10776

Vector Data Basics

A number of common functions have methods for spatial data

silty = subset(soils, Silt1 > 70)
paste("There are", length(soils), "soil features total;")
## [1] "There are 75 soil features total;"
paste(length(silty), "with a silt percentage over 70")
## [1] "12 with a silt percentage over 70"

Vector Data Basics

Making simple maps is quite easy

par(mfrow=c(2,1), bg=NA)
plot(
    soils,
    main="Soils Polygons",
    col=rainbow(5))
plot(
    wells,
    main="Well Data",
    col='red'
)












Coordinate Reference Systems

A (Very) Brief Break

A coordinate reference system (CRS) defines the surface of the world. There are many and if they don't match, errors and issues can arise

Coordinate Reference Systems

A (Very) Brief Break

To illustrate issues:

soils = readOGR(
    dsn="data",
    layer="soilsData")
plot(
    soils,
    main="Soils",
    col=rainbow(5)
)
plot(
    wells,
    add=T
)












Hmmm, where are the points?

  • plot the two, brief discuss issues with CRS matching

  • Example scenario, demo gIntersects and how to use introduce other types of spatial relations

  • Use over to extract attributes and select those above a threshold of sand

  • Introduce buffering and suggest trying with that

Outline 3

Part II

  • introduce ward data

  • scenario for modeling: predict %dem turnout

  • use regular linear regression, moran I the residuals

  • construct neighborhood weights using adjacency and distance, then construct model

  • take a look at results

Outline 4

Part III

  • Scenario create map of %dem with indication of percent turnout.

  • Walk throug various iterations, raise problems then solve

  • plot just lines

  • introduce thematic mapping/choropleth mapping/data classification and coloring

  • Show classInt and creating the color vector

  • legend manipulation

  • creating centroids and scaling proportionally

Raster Data

Intro

A raster grid is rectangular.

Grid is another word for matrix.

Grid is another word for image.

A GIS raster grid is a matrix/image with an associated location and projection.

Intro

At a minimum, a GIS raster grid contains:

  1. matrix of values
  2. projection
  3. reference point, often (x,y) of the lower-left corner
  4. cellsize









Raster I/O

The rgdal rgdal packages is primarily for I/O and projecting GIS data

library(rgdal)

The raster package does everything rgdal does, but it includes lots of additional functionality.

library(raster)

Raster I/O

elev = readGDAL("data/dem_wi.tif")
writeGDAL(elev, "data/dem_wi_out.tif")
elev = raster("data/dem_wi.tif")
writeRaster(elev, "data/dem_wi_out.tif")

Raster data structure

The raster object elev has all the necessary pieces of spatial information:

elev
## class       : RasterLayer 
## dimensions  : 284, 387, 109908  (nrow, ncol, ncell)
## resolution  : 0.01666667, 0.01666667  (x, y)
## extent      : -93.03262, -86.58262, 42.3949, 47.12823  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## data source : /home/devans/Documents/GeRgraphyPresentation/data/dem_wi.tif 
## names       : dem_wi 
## values      : 175, 565.4104  (min, max)

Raster data structure

Which means we can make a map!

m = leaflet() %>%
  addTiles() %>%
  addRasterImage(elev, opacity=0.5)
m

Raster data structure

Raster analysis

Remember that rasters are just matrices!

Therefore, most matrix operations can be applied to rasters. For example:

plot(
  elev > 400,
  col=c("red", "blue")
)








Raster analysis

Rasters can be easily converted to matrices to do more complex work.

lat_grad = apply(
  as.matrix(elev),
  1,
  mean,
  na.rm=T
)
plot(lat_grad, type="l")






Raster overlay

Most raster analysis ultimately executes some sort of overlay.

The issue:

To overlay two or more rasters, their projections, extents, and cellsizes must align perfectly.

This can be a difficult task.

Raster overlay

coordinate systems

What is the highest point in each county?

# Pseudo-code
1. Read in elevation data (raster grid)
2. Read in county boundary data (polygons)
3. Convert counties to raster grid that aligns with elevation grid
4. Find maximum elevation gridcell within each county

Raster overlay

coordinate systems

counties = readOGR("data", "WI_Counties")
## OGR data source with driver: ESRI Shapefile 
## Source: "data", layer: "WI_Counties"
## with 72 features
## It has 7 fields
elev
## class       : RasterLayer 
## dimensions  : 284, 387, 109908  (nrow, ncol, ncell)
## resolution  : 0.01666667, 0.01666667  (x, y)
## extent      : -93.03262, -86.58262, 42.3949, 47.12823  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## data source : /home/devans/Documents/GeRgraphyPresentation/data/dem_wi.tif 
## names       : dem_wi 
## values      : 175, 565.4104  (min, max)

Raster overlay

coordinate systems

proj4string(counties)
## [1] "+proj=tmerc +lat_0=0 +lon_0=-90 +k=0.9996 +x_0=520000 +y_0=-4480000 +ellps=GRS80 +units=m +no_defs"
proj4string(elev)
## [1] "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"

Raster overlay

coordinate systems

extent(counties)
## class       : Extent 
## xmin        : 294839 
## xmax        : 770036.4 
## ymin        : 225108.8 
## ymax        : 734398.4
extent(elev)
## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

cty_grid = rasterize(counties, elev, field="COUNTY_FIP")
summary(cty_grid)
##          layer
## Min.        NA
## 1st Qu.     NA
## Median      NA
## 3rd Qu.     NA
## Max.        NA
## NA's    109908

Raster overlay

coordinate systems

prj = proj4string(elev)
cty_prj = spTransform(counties, prj)
To do this, we use the spTransform function in the sp package.

Raster overlay

coordinate systems

extent(cty_prj)
## class       : Extent 
## xmin        : -92.88924 
## xmax        : -86.8048 
## ymin        : 42.49197 
## ymax        : 47.08077
extent(elev)
## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

plot(elev)
plot(cty_prj, add=TRUE)














Raster overlay

coordinate systems

cty_grid = rasterize(counties, elev, field="COUNTY_FIP")
summary(cty_grid)
##          layer
## Min.        NA
## 1st Qu.     NA
## Median      NA
## 3rd Qu.     NA
## Max.        NA
## NA's    109908

Raster overlay

coordinate systems

extent(cty_grid)
## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823
extent(elev)
## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

library(dplyr)
ovly = data.frame(
  elev=getValues(elev),
  cty=getValues(cty_grid)
)

hi_pt = ovly %>%
  group_by(cty) %>%
  mutate(
    elev = (elev == max(elev, na.rm=T)) * elev
  ) %>%
  ungroup()

elev = setValues(elev, hi_pt[["elev"]])
elev[elev == 0] = NA
hi_pt_sp = rasterToPoints(elev, spatial=T)

Raster overlay

coordinate systems